Solve for $x$ and $y$ using elimination. ${3x+2y = 13}$ ${-2x-2y = -12}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {3x+2y = 13}\thinspace$ to find $y$ ${3}{(1)}{ + 2y = 13}$ $3+2y = 13$ $3{-3} + 2y = 13{-3}$ $2y = 10$ $\dfrac{2y}{{2}} = \dfrac{10}{{2}}$ ${y = 5}$ You can also plug ${x = 1}$ into $\thinspace {-2x-2y = -12}\thinspace$ and get the same answer for $y$ : ${-2}{(1)}{ - 2y = -12}$ ${y = 5}$